The first step computes a minimum reference return and nine deciles. The input x must be a matrix having p columns (with a name for each column) and n rows as in the data. If data are missing for some columns, insert NA's. Thus x has p column of the data matrix ready for comparison and ranking. For example, x has a matrix of stock returns. The output matrix produced by this function also has p columns for each column (i.e., for each stock being compared). The output matrix has nineteen rows. The top nine rows have the magnitudes of deciles. Rows 10 to 18 have respective ranks of the decile magnitudes. The next (19-th) row of the output reports a weighted sum of ranks. Ranking always gives the smallest number 1 to the most desirable outcome. We suggest that a higher portfolio weight be given to the column having smallest rank value (along the 19th line). The 20-th row further ranks the weighted sums of ranks in row 19. Investor should choose the stock (column) representing the smallest rank value along the last (20th) row of the ‘out’ matrix.
decileVote(mtx, howManySd = 0.1)
(n X p) matrix of data. For example, returns on p stocks n months
used to define ‘fixmin’= imaginary lowest return defined by going howManySd=default=0.1 maximum of standard deviations of all stocks below the minimum return for all stocks in the data
out is a matrix with p columns (same as in the input matrix) and twenty rows. Top nine rows have 9 deciles, next nine rows have their ranks. The 19-th row of ‘out’ has a weighted sum of 9 ranks. All columns refer to one stock. The weighted sum for each stock is then ranked. A portfolio manager is assumed to prefer higher return represented by high decile values represented by the column with the largest weighted sum. can give largest weight to the column with the smallest bottom line. The bottom line (20-th) labeled “choice" of the ‘out’ matrix is defined so that choice =1 suggests the stock deserving the highest weight in the portfolio. The portfolio manager will generally give the lowest weight (=0?) to the stock representing column having number p as the choice number. The manager may want to sell this stock. Another output of the ‘decileVote’ function is ‘fixmin’ representing the smallest possible return of all the stocks in the input ‘mtx’ of returns. It is useful as a reference stock. We compute stochastic dominance numbers for each stock with this imaginary stock yielding fixmin return for all time periods.
Prof. H. D. Vinod, Economics Dept., Fordham University, NY
x1=c(1,4,7,2,6) x2=c(3,4,8,4,7) decileVote(cbind(x1,x2))
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